Complexes of Injective Words and Their Commutation Classes

TL;DR

This paper investigates the structure of Boolean cell complexes formed by injective words over a finite alphabet and explores their commutation classes, extending prior research on related combinatorial complexes.

Contribution

It generalizes previous work by Farmer and Bj"orner and Wachs on injective word complexes to include their commutation classes.

Findings

Characterization of complexes of injective words

Analysis of their commutation classes

Extension of existing combinatorial frameworks

Abstract

Let $S$ be a finite alphabet. An injective word over $S$ is a word over $S$ such that each letter in $S$ appears at most once in the word. We study Boolean cell complexes of injective words over $S$ and their commutation classes. This generalizes work by Farmer and by Bj\"orner and Wachs on the complex of all injective words.